Problem: Solve for $x$ and $y$ using elimination. ${5x-3y = 1}$ ${2x+3y = 34}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $7x = 35$ $\dfrac{7x}{{7}} = \dfrac{35}{{7}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-3y = 1}\thinspace$ to find $y$ ${5}{(5)}{ - 3y = 1}$ $25-3y = 1$ $25{-25} - 3y = 1{-25}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {2x+3y = 34}\thinspace$ and get the same answer for $y$ : ${2}{(5)}{ + 3y = 34}$ ${y = 8}$